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Further results on super graceful labeling of graphs
AKCE International Journal of Graphs and Combinatorics, 2016 Let G=(V(G),E(G)) be a simple, finite and undirected graph of order p and size q. A bijection f:V(G)∪E(G)→{k,k+1,k+2,…,k+p+q−1} such that f(uv)=|f(u)−f(v)| for every edge uv∈E(G) is said to be a k-super graceful labeling of G.
Gee-Choon Lau, Wai Chee Shiu, Ho-Kuen Ng
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A survey and a new class of graceful unicylic graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A graph G admits a graceful labeling if there is a one-to-one map f from the set of vertices of G to such that when an edge xy is assigned the label the resulting set of edge labels is When such a labeling exists, G is called graceful. Rosa showed that a
Max Pambe Biatch’ +2 more
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Computer search for graceful labeling: a survey
Electronic Journal of Graph Theory and Applications, 2022 This paper surveys the main computer search results for finding graceful labeling of trees. The paper is devoted to the memory of Mirka Miller, who made an outstanding contribution to the area of graph labeling.
Ljiljana Brankovic, Michael J. Reynolds
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On edge-graceful labeling and deficiency for regular graphs
AKCE International Journal of Graphs and Combinatorics, 2018 An edge-graceful labeling of a finite simple graph with vertices and edges is a bijection from the set of edges to the set of integers such that the vertex sums are pairwise distinct modulo , where the vertex sum at a vertex is the sum of labels of all ...
Tao-Ming Wang, Guang-Hui Zhang
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Additively graceful signed graphs
AKCE International Journal of Graphs and Combinatorics, 2023 Let [Formula: see text] be a signed graph of order p and size q. Let [Formula: see text] and [Formula: see text] Let [Formula: see text] be an injective function and let [Graphic: see text]gf(uv)={|f(u)−f(v)| if uv∈E+f(u)+f(v) if uv∈E−The function f is ...
Jessica Pereira +2 more
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Graceful labeling of digraphs—a survey
AKCE International Journal of Graphs and Combinatorics, 2021 A digraph D with p vertices and q arcs is labeled by assigning a distinct integer value g(v) from to each vertex v. The vertex values, in turn, induce a value g(u, v) on each arc (u, v) where g(u, v) = (g(v) − g(u)) (mod q + 1) If the arc values are all ...
Shivarajkumar, M. A. Sriraj, S. M. Hegde
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Generating graceful unicyclic graphs from a given forest
AKCE International Journal of Graphs and Combinatorics, 2020 Acharya (1982) proved that every connected graph can be embedded in a graceful graph. The generalization of this result that, any set of graphs can be packed into a graceful graph was proved by Sethuraman and Elumalai (2005). Recently, Sethuraman et al. (
G. Sethuraman, V. Murugan
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GRACEFUL LABELING OF HANGING THETA GRAPHS [PDF]
International Journal of Pure and Apllied Mathematics, 2013 Summary: In this paper, we introduce a new class of hanging theta graphs and prove that those graphs admit graceful labeling.
Janakiraman, T. N., Sathiamoorthy, G.
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Construction of an -labeled tree from a given set of -labeled trees
AKCE International Journal of Graphs and Combinatorics, 2017 Inspired by the method of Koh et al. (1979) of combining known graceful trees to construct bigger graceful trees, a new class of graceful trees is constructed from a set of known graceful trees, in a specific way.
G. Sethuraman, P. Ragukumar
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, 2020 A graceful labeling of a graph $G$ with $m$ edges consists of labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that, when each edge is assigned as induced label the absolute difference of the labels of its endpoints, all induced ...
Dantas, Simone +2 more
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